A computer specialist who deleted Hillary Clinton’s emails despite orders from Congress to preserve them was given immunity by the Justice Department during its investigation into her personal email account, according to a law enforcement official and others briefed on the investigation.

Republicans have called for the department to investigate the deletions, but the immunity deal with the specialist, Paul Combetta, makes it unlikely that the request will go far. Representative Jason Chaffetz of Utah, the top Republican on the House oversight committee, asked the Justice Department on Tuesday to investigate whether Mrs. Clinton, her lawyers or the specialist obstructed justice when the emails were deleted in March 2015.

Mr. Combetta is one of at least two people who were given immunity by the Justice Department as part of the investigation. The other was Bryan Pagliano, a former campaign staff member for Mrs. Clinton’s 2008 presidential campaign, who was granted immunity in exchange for answering questions about how he set up a server in Mrs. Clinton’s home in Chappaqua, N.Y., around the time she became secretary of state in 2009.